A low complexity model order and frequency estimation of multiple 2-D complex sinusoids

Abstract

Model order and frequency estimation of multiple 2-D complex sinusoids in additive white Gaussian noise are addressed. Frequency estimation follows the coarse-fine search strategy. Coarse estimates, obtained by locating maxima of the 2-D discrete Fourier transform, are refined in a two-stage procedure. In both stages, frequency refinement is based on three-point periodogram maximization. In order to provide accurate model order estimation (MOE) for a wide signal-to-noise ratio (SNR) range, our approach combines two metrics for sinusoid detection in the 2-D frequency domain, one for low and the other for high SNR values. The proposed frequency estimation method attains the Cramér-Rao lower bound and it outperforms parametric methods in terms of the estimation accuracy and numerical efficiency. Compared with information criterion-based methods, the proposed MOE approach is numerically more efficient, it does not require estimation of noise variance and hence does not suffer from overestimation at high SNR.